Question: What is the inverse of $f(x)=4-5x$?
Explanation: If we let $g(x)$ denote the inverse to $f$ then we can evaluate $f$ at $g(x)$ to get  \[f(g(x))=4-5g(x).\]Since $g$ is the inverse to $f$, the left side is $x$ and  \[x=4-5g(x).\]Solving for $g(x)$, we find $g(x) = \boxed{\frac{4-x}{5}}$.